1 | |
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2 | ! |
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3 | ! This program may be freely redistributed under the |
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4 | ! condition that the copyright notices (including this |
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5 | ! entire header) are not removed, and no compensation |
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6 | ! is received through use of the software. Private, |
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7 | ! research, and institutional use is free. You may |
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8 | ! distribute modified versions of this code UNDER THE |
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9 | ! CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE |
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10 | ! TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE |
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11 | ! ORIGINAL AUTHOR, BOTH SOURCE AND OBJECT CODE ARE |
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12 | ! MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR |
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13 | ! NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution |
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14 | ! of this code as part of a commercial system is |
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15 | ! permissible ONLY BY DIRECT ARRANGEMENT WITH THE |
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16 | ! AUTHOR. (If you are not directly supplying this |
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17 | ! code to a customer, and you are instead telling them |
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18 | ! how they can obtain it for free, then you are not |
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19 | ! required to make any arrangement with me.) |
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20 | ! |
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21 | ! Disclaimer: Neither I nor: Columbia University, the |
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22 | ! National Aeronautics and Space Administration, nor |
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23 | ! the Massachusetts Institute of Technology warrant |
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24 | ! or certify this code in any way whatsoever. This |
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25 | ! code is provided "as-is" to be used at your own risk. |
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26 | ! |
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27 | ! |
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28 | |
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29 | ! |
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30 | ! WENO1D.f90: WENO-style slope-limiting for 1d reconst. |
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31 | ! |
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32 | ! Darren Engwirda |
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33 | ! 08-Sep-2016 |
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34 | ! de2363 [at] columbia [dot] edu |
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35 | ! |
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36 | ! |
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37 | |
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38 | pure subroutine wenoi (npos,delx,oscl,ipos, & |
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39 | & ivar,halo,& |
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40 | & wlim,wval ) |
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41 | |
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42 | ! |
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43 | ! NPOS no. edges over grid. |
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44 | ! DELX grid-cell spacing array. SIZE(DELX) == +1 if |
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45 | ! the grid is uniformly spaced . |
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46 | ! OSCL cell-centred oscillation-detectors, where OSCL |
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47 | ! has SIZE = +2-by-NVAR-by-NPOS-1. OSCL is given |
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48 | ! by calls to OSCLI(). |
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49 | ! IPOS grid-cell index for which to calc. weights . |
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50 | ! IVAR state-var index for which to calc/ weights . |
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51 | ! HALO width of recon. stencil, symmetric about IPOS . |
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52 | ! WLIM limiter treatment at endpoints, monotonic or |
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53 | ! otherwise . |
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54 | ! WVAL WENO weights vector, such that FHAT = WVAL(1) * |
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55 | ! UHAT + WVAL(2) * LHAT, where UHAT and LHAT are |
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56 | ! the unlimited and monotonic grid-cell profiles |
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57 | ! respectively . |
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58 | ! |
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59 | |
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60 | implicit none |
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61 | |
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62 | !------------------------------------------- arguments ! |
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63 | integer, intent(in) :: npos,halo |
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64 | integer, intent(in) :: ipos,ivar |
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65 | integer, intent(in) :: wlim |
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66 | real*8 , intent(in) :: delx(:) |
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67 | real*8 , intent(in) :: oscl(:,:,:) |
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68 | real*8 , intent(out) :: wval(2) |
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69 | |
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70 | !------------------------------------------- variables ! |
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71 | real*8 :: omin,omax,wsum |
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72 | |
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73 | real*8 , parameter :: ZERO = +1.d-16 |
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74 | |
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75 | if (size(delx).gt.+1) then |
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76 | |
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77 | !------------------- use variable grid spacing variant ! |
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78 | |
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79 | call wenov(npos,delx,oscl, & |
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80 | & ipos,ivar,halo, & |
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81 | & wlim,omin,omax) |
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82 | |
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83 | else |
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84 | |
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85 | !------------------- use constant grid spacing variant ! |
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86 | |
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87 | call wenoc(npos,delx,oscl, & |
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88 | & ipos,ivar,halo, & |
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89 | & wlim,omin,omax) |
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90 | |
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91 | end if |
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92 | |
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93 | !------------------ compute WENO-style profile weights ! |
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94 | |
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95 | omax = omax + ZERO |
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96 | omin = omin + ZERO |
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97 | |
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98 | if (halo .ge. +3) then |
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99 | |
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100 | wval(1) = +1.0d+7 / omax ** 3 |
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101 | wval(2) = +1.0d+0 / omin ** 3 |
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102 | |
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103 | else & |
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104 | & if (halo .le. +2) then |
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105 | |
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106 | wval(1) = +1.0d+5 / omax ** 3 |
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107 | wval(2) = +1.0d+0 / omin ** 3 |
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108 | |
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109 | end if |
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110 | |
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111 | wsum = wval(1) + wval(2) + ZERO |
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112 | wval(1) = wval(1) / wsum |
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113 | ! wval(2) = wval(2) / wsum |
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114 | wval(2) =-wval(1) + 1.d0 ! wval(2)/wsum but robust ! |
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115 | |
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116 | return |
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117 | |
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118 | end subroutine |
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119 | |
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120 | pure subroutine wenov (npos,delx,oscl,ipos, & |
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121 | & ivar,halo,& |
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122 | & wlim,omin,omax) |
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123 | |
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124 | ! |
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125 | ! *this is the variable grid-spacing variant . |
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126 | ! |
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127 | ! NPOS no. edges over grid. |
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128 | ! DELX grid-cell spacing array. SIZE(DELX) == +1 if |
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129 | ! the grid is uniformly spaced . |
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130 | ! OSCL cell-centred oscillation-detectors, where OSCL |
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131 | ! has SIZE = +2-by-NVAR-by-NPOS-1. OSCL is given |
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132 | ! by calls to OSCLI(). |
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133 | ! IPOS grid-cell index for which to calc. weights . |
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134 | ! IVAR state-var index for which to calc/ weights . |
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135 | ! HALO width of recon. stencil, symmetric about IPOS . |
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136 | ! WLIM limiter treatment at endpoints, monotonic or |
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137 | ! otherwise . |
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138 | ! OMIN min. and max. oscillation indicators over the |
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139 | ! OMAX local re-con. stencil . |
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140 | ! |
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141 | |
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142 | implicit none |
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143 | |
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144 | !------------------------------------------- arguments ! |
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145 | integer, intent(in) :: npos,halo |
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146 | integer, intent(in) :: ipos,ivar |
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147 | integer, intent(in) :: wlim |
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148 | real*8 , intent(in) :: delx(:) |
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149 | real*8 , intent(in) :: oscl(:,:,:) |
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150 | real*8 , intent(out) :: omin,omax |
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151 | |
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152 | !------------------------------------------- variables ! |
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153 | integer :: hpos |
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154 | integer :: head,tail |
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155 | integer :: imin,imax |
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156 | real*8 :: deli,delh |
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157 | real*8 :: hh00,hsqr |
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158 | real*8 :: dfx1,dfx2 |
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159 | real*8 :: oval |
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160 | |
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161 | !------------------- calc. lower//upper stencil bounds ! |
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162 | |
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163 | head = 1; tail = npos - 1 |
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164 | |
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165 | if(wlim.eq.mono_limit) then |
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166 | |
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167 | !---------------------- deactivate WENO at boundaries ! |
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168 | |
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169 | if (ipos-halo.lt.head) then |
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170 | |
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171 | omax = 1.d0 |
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172 | omin = 0.d0 ; return |
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173 | |
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174 | end if |
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175 | |
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176 | if (ipos+halo.gt.tail) then |
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177 | |
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178 | omax = 1.d0 |
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179 | omin = 0.d0 ; return |
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180 | |
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181 | end if |
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182 | |
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183 | end if |
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184 | |
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185 | !---------------------- truncate stencil at boundaries ! |
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186 | |
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187 | imin = max(ipos-halo,head) |
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188 | imax = min(ipos+halo,tail) |
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189 | |
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190 | !------------------ find min/max indicators on stencil ! |
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191 | |
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192 | dfx1 = oscl(1,ivar,ipos) |
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193 | dfx2 = oscl(2,ivar,ipos) |
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194 | |
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195 | hh00 = delx(ipos+0)**1 |
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196 | hsqr = delx(ipos+0)**2 |
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197 | |
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198 | oval =(hh00 * dfx1)**2 & |
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199 | & +(hsqr * dfx2)**2 |
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200 | |
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201 | omin = oval |
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202 | omax = oval |
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203 | |
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204 | !---------------------------------------- "lower" part ! |
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205 | |
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206 | delh = 0.d0 |
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207 | |
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208 | do hpos = ipos-1, imin, -1 |
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209 | |
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210 | !------------------ calc. derivatives centred on IPOS. ! |
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211 | |
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212 | deli = delx(hpos+0) & |
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213 | & + delx(hpos+1) |
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214 | |
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215 | delh = delh + deli*.5d0 |
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216 | |
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217 | dfx1 = oscl(1,ivar,hpos) |
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218 | dfx2 = oscl(2,ivar,hpos) |
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219 | |
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220 | dfx1 = dfx1 + dfx2*delh |
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221 | |
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222 | !------------------ indicator: NORM(H^N * D^N/DX^N(F)) ! |
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223 | |
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224 | oval = (hh00 * dfx1)**2 & |
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225 | & + (hsqr * dfx2)**2 |
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226 | |
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227 | if (oval .lt. omin) then |
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228 | omin = oval |
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229 | else & |
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230 | & if (oval .gt. omax) then |
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231 | omax = oval |
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232 | end if |
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233 | |
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234 | end do |
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235 | |
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236 | !---------------------------------------- "upper" part ! |
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237 | |
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238 | delh = 0.d0 |
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239 | |
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240 | do hpos = ipos+1, imax, +1 |
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241 | |
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242 | !------------------ calc. derivatives centred on IPOS. ! |
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243 | |
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244 | deli = delx(hpos+0) & |
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245 | & + delx(hpos-1) |
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246 | |
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247 | delh = delh - deli*.5d0 |
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248 | |
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249 | dfx1 = oscl(1,ivar,hpos) |
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250 | dfx2 = oscl(2,ivar,hpos) |
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251 | |
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252 | dfx1 = dfx1 + dfx2*delh |
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253 | |
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254 | !------------------ indicator: NORM(H^N * D^N/DX^N(F)) ! |
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255 | |
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256 | oval = (hh00 * dfx1)**2 & |
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257 | & + (hsqr * dfx2)**2 |
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258 | |
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259 | if (oval .lt. omin) then |
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260 | omin = oval |
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261 | else & |
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262 | & if (oval .gt. omax) then |
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263 | omax = oval |
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264 | end if |
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265 | |
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266 | end do |
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267 | |
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268 | return |
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269 | |
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270 | end subroutine |
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271 | |
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272 | pure subroutine wenoc (npos,delx,oscl,ipos, & |
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273 | & ivar,halo,& |
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274 | & wlim,omin,omax) |
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275 | |
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276 | ! |
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277 | ! *this is the constant grid-spacing variant . |
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278 | ! |
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279 | ! NPOS no. edges over grid. |
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280 | ! DELX grid-cell spacing array. SIZE(DELX) == +1 if |
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281 | ! the grid is uniformly spaced . |
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282 | ! OSCL cell-centred oscillation-detectors, where OSCL |
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283 | ! has SIZE = +2-by-NVAR-by-NPOS-1. OSCL is given |
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284 | ! by calls to OSCLI(). |
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285 | ! IPOS grid-cell index for which to calc. weights . |
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286 | ! IVAR state-var index for which to calc/ weights . |
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287 | ! HALO width of recon. stencil, symmetric about IPOS . |
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288 | ! WLIM limiter treatment at endpoints, monotonic or |
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289 | ! otherwise . |
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290 | ! OMIN min. and max. oscillation indicators over the |
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291 | ! OMAX local re-con. stencil . |
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292 | ! |
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293 | |
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294 | implicit none |
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295 | |
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296 | !------------------------------------------- arguments ! |
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297 | integer, intent(in) :: npos,halo |
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298 | integer, intent(in) :: ipos,ivar |
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299 | integer, intent(in) :: wlim |
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300 | real*8 , intent(in) :: delx(1) |
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301 | real*8 , intent(in) :: oscl(:,:,:) |
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302 | real*8 , intent(out) :: omin,omax |
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303 | |
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304 | !------------------------------------------- variables ! |
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305 | integer :: hpos |
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306 | integer :: head,tail |
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307 | integer :: imin,imax |
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308 | real*8 :: delh |
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309 | real*8 :: dfx1,dfx2 |
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310 | real*8 :: oval |
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311 | |
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312 | !------------------- calc. lower//upper stencil bounds ! |
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313 | |
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314 | head = 1; tail = npos - 1 |
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315 | |
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316 | if(wlim.eq.mono_limit) then |
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317 | |
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318 | !---------------------- deactivate WENO at boundaries ! |
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319 | |
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320 | if (ipos-halo.lt.head) then |
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321 | |
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322 | omax = 1.d0 |
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323 | omin = 0.d0 ; return |
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324 | |
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325 | end if |
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326 | |
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327 | if (ipos+halo.gt.tail) then |
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328 | |
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329 | omax = 1.d0 |
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330 | omin = 0.d0 ; return |
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331 | |
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332 | end if |
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333 | |
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334 | end if |
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335 | |
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336 | !---------------------- truncate stencil at boundaries ! |
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337 | |
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338 | imin = max(ipos-halo,head) |
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339 | imax = min(ipos+halo,tail) |
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340 | |
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341 | !------------------ find min/max indicators on stencil ! |
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342 | |
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343 | dfx1 = oscl(1,ivar,ipos) |
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344 | dfx2 = oscl(2,ivar,ipos) |
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345 | |
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346 | oval = (2.d0**1*dfx1)**2 & |
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347 | & + (2.d0**2*dfx2)**2 |
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348 | |
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349 | omin = oval |
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350 | omax = oval |
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351 | |
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352 | !---------------------------------------- "lower" part ! |
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353 | |
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354 | delh = 0.d0 |
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355 | |
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356 | do hpos = ipos-1, imin, -1 |
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357 | |
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358 | !------------------ calc. derivatives centred on IPOS. ! |
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359 | |
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360 | delh = delh + 2.d0 |
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361 | |
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362 | dfx1 = oscl(1,ivar,hpos) |
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363 | dfx2 = oscl(2,ivar,hpos) |
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364 | |
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365 | dfx1 = dfx1 + dfx2*delh |
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366 | |
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367 | !------------------ indicator: NORM(H^N * D^N/DX^N(F)) ! |
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368 | |
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369 | oval = (2.d0**1*dfx1)**2 & |
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370 | & + (2.d0**2*dfx2)**2 |
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371 | |
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372 | if (oval .lt. omin) then |
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373 | omin = oval |
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374 | else & |
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375 | & if (oval .gt. omax) then |
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376 | omax = oval |
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377 | end if |
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378 | |
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379 | end do |
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380 | |
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381 | !---------------------------------------- "upper" part ! |
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382 | |
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383 | delh = 0.d0 |
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384 | |
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385 | do hpos = ipos+1, imax, +1 |
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386 | |
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387 | !------------------ calc. derivatives centred on IPOS. ! |
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388 | |
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389 | delh = delh - 2.d0 |
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390 | |
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391 | dfx1 = oscl(1,ivar,hpos) |
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392 | dfx2 = oscl(2,ivar,hpos) |
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393 | |
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394 | dfx1 = dfx1 + dfx2*delh |
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395 | |
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396 | !------------------ indicator: NORM(H^N * D^N/DX^N(F)) ! |
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397 | |
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398 | oval = (2.d0**1*dfx1)**2 & |
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399 | & + (2.d0**2*dfx2)**2 |
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400 | |
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401 | if (oval .lt. omin) then |
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402 | omin = oval |
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403 | else & |
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404 | & if (oval .gt. omax) then |
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405 | omax = oval |
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406 | end if |
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407 | |
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408 | end do |
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409 | |
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410 | return |
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411 | |
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412 | end subroutine |
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413 | |
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414 | |
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415 | |
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